The Large Margin Mechanism for Differentially Private Maximization

A basic problem in the design of privacy-preserving algorithms is the private maximization problem: the goal is to pick an item from a universe that (approximately) maximizes a data-dependent function, all under the constraint of differential privacy. This problem has been used as a sub-routine in many privacy-preserving algorithms for statistics and machine-learning. Previous algorithms for this problem are either range-dependent—i.e., their utility diminishes with the size of the universe—or only apply to very restricted function classes. This work provides the first general-purpose, range-independent algorithm for private maximization that guarantees approximate differential privacy. Its applicability is demonstrated on two fundamental tasks in data mining and machine learning.